How to Suppress Random Effects and Retain AR(1) Correlation Structure in R's lme Mixed Model

Описание: Learn how to suppress random effects while maintaining the AR(1) correlation structure in R's lme mixed model using generalized least squares (gls).
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This video is based on the question https://stackoverflow.com/q/75990524/ asked by the user 'Neal Oden' ( https://stackoverflow.com/u/8903453/ ) and on the answer https://stackoverflow.com/a/75990676/ provided by the user 'Ben Bolker' ( https://stackoverflow.com/u/190277/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Understanding the Problem of Random Effects in Mixed Models

When working with mixed models in R, particularly when re-creating analyses from other software such as SAS, you may encounter specific issues. A common problem arises when you want to suppress random effects while still retaining the AR(1) correlation structure. This issue is particularly relevant when transitioning from SAS to R using the lme function. The core question is: How can you do this effectively in R?

The SAS Mixed Model Structure

To provide some context, consider the SAS mixed model outlined in the initial question. Here’s a simplified version of what it looks like:

[[See Video to Reveal this Text or Code Snippet]]

In this SAS code:

Each PATID gets a random intercept which accounts for individual variability.

There is also a repeated measures aspect with an AR(1) correlation structure. This structure considers that the correlation between measurements decreases as the time between them increases.

Re-Creating the Model in R

Using R's lme function, one might typically set up the model as follows:

[[See Video to Reveal this Text or Code Snippet]]

In this setup, both random effects and correlation structures are defined. However, what if you want to drop the random effects but still maintain the AR(1) correlation structure?

The Challenge with R's lme Function

When you attempt to drop the random statement in R, this leads to an error depicting incompatible formulas for groups in 'random' and 'correlation'. The desired model structure cannot be achieved using lme alone for the specific aim of suppressing random effects.

Solution: Use Generalized Least Squares (GLS)

As suggested by community insights, the best alternative would be to use the gls (Generalized Least Squares) function rather than lme. This allows you to fit a model that includes heteroscedasticity or correlation without random effects.

Setting Up the gls Model

Here’s how you would set this up using the gls function:

[[See Video to Reveal this Text or Code Snippet]]

Example with Provided Data

To further clarify, let’s consider an example using existing R datasets. Here’s a practical demonstration using the sleepstudy dataset from the lme4 package:

[[See Video to Reveal this Text or Code Snippet]]

In this instance, you can still model the effect of days on reaction time while appropriately managing the correlation without the need for random effects.

Key Takeaways

Switch to GLS: If you need to suppress random effects while retaining correlation structures in your model, the gls function is your best option.

Model Structure: Ensure you properly set the model with the correct formatting as gls() expects a different argument structure than lme().

Practical Examples: Use built-in datasets to test and explore these functions to solidify your understanding.

By following these steps, you will be well-equipped to conduct mixed models analyses in R while navigating the challenges that arise from differences in software capabilities.